The paper studies three developments of a class of near-maximum-likelihood detection processes derived from a conventional nonlinear (decision feedback) equaliser. The new detectors are suitable for binary signals transmitted over a linear baseband channel introducing severe amplitude distortion. The complexity of the processes is not excessive, and increases approximately linearly with the delay in detection. Thus, a sufficiently large delay in detection can be employed to achieve a near-optimum tolerance to noise when the received signal has been very severely distorted. The paper describes three novel detection processes, and presents the results of computer simulation tests, comparing the tolerances to additive white Gaussian noise of various arrangements of each detector with that of the optimum detector of the given class and that of a conventional nonlinear equaliser. Three different channels are used in the tests and binary signals are transmitted in every case.